Zusammenfassung (Englisch)

During the last decade, there has been an increasing interest in the physics of solid-state systems whose low-energy excitations can be treated as Dirac fermions, that is, fermions described by the Dirac equation. Nowadays, the prime examples for such systems are graphene, whose band structure can be approximated by a two-dimensional (2D) Dirac-like Hamiltonian in the vicinity of the K and K' ...

Zusammenfassung (Englisch)

During the last decade, there has been an increasing interest in the physics of solid-state systems whose low-energy excitations can be treated as Dirac fermions, that is, fermions described by the Dirac equation. Nowadays, the prime examples for such systems are graphene, whose band structure can be approximated by a two-dimensional (2D) Dirac-like Hamiltonian in the vicinity of the K and K' points, and topological insulators, which possess edge states with a linear, one-dimensional (1D) spectrum in the case of 2D systems and surface states described by a single Dirac cone in the case of three-dimensional (3D) topological insulators. One of the main reasons for the enormous interest in these materials is that they offer the possibility to study quantum electrodynamical phenomena in solid-state systems.

In the first part of this thesis, we theoretically study magnetic properties of inverted HgTe/CdTe quantum wells, a system which constitutes a 2D topological insulator. In particular, we study the crossover between the quantum spin Hall and quantum Hall states in those structures using analytical as well as numerical methods. Moreover, the bulk magnetic susceptibility is investigated and found to exhibit characteristic de Haas-van Alphen oscillations. Finally, the bulk magneto-optical conductivity is calculated. Here, we find that for large magnetic fields, when the spacing between neighboring Landau levels is large compared to the lifetime broadening, one can observe pronounced peaks and oscillations in the magneto-optical conductivity.

In the second part the thesis, we investigate the effect that intrinsic graphene optical as well as surface polar phonons (SPPs) have on the optical conductivity in graphene using the Kubo linear response formalism. Here, we observe an increase of the absorption in the optical gap due to electron-phonon coupling.

The third part of this thesis is devoted to another topic of recent interest in solid-state physics, namely the field of spin caloritronics. Here, we generalize the standard model of spin injection to describe the coupling between charge, spin, and heat transport in metals. The formalism is then used to analyze several different structures consisting of ferromagnetic (F) and normal (N) metals, such as F/N and F/N/F junctions.